2012/10/22 by Sergey Simonov, Simonov, Sergey, Harald Woracek +1
Mathematics · #34B20 #34B45 #34L40 #47E05 #FOS: Mathematics #Spectral Theory (math.SP) #math.SP #msc:34B20 #msc:34B45 #msc:34L40 #msc:47E05
paper · pdf · doi:10.48550/arxiv.1210.5966
arxiv created 2012/10/22 · arxiv updated 2012/10/23
We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schroedinger operator on a star-shaped graph with continuity and Kirchhoff conditions at the interior vertex. We compute the multiplicity of the singular spectrum in terms of the spectral measures of the Weyl functions associated with the single (independently considered) boundary relations. This result is a generalization and refinement of Theorem of I.S. Kac.